Abstract
The comparative efficiency of different algorithms of statistical modelling of polarized radiation transfer process is studied for the problem with molecular matrix of scattering. The vector illumination and brightness are calculated for passing and reflected radiation. A statistical nuclear estimator is developed for evaluation of the corresponding angular distributions taking into account the weights of registered quanta.
Funding: The work was supported by the Russian Foundation for Basic Research (projects 16–01–0530 a, 17–01–00823 a, 18–01–00356 a, 18–31–00213 mol, 16–01–00145 a, 18–01–00609 a).
References
[1] S. Bartel and A. H. Hielscher, Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media. Applied Optics39 (2000), No. 10, 1580–1588.10.1364/AO.39.001580Suche in Google Scholar
[2] A. A. Borovkov, Mathematical Statistic. Nauka, Novosibirsk, 1997 (in Russian).Suche in Google Scholar
[3] S. Chandrasekhar, Radiative Transfer. Oxford, 1950.Suche in Google Scholar
[4] H. Cramer, Mathematical Methods of Statistics. Princeton Univ. Press, USA, 1946.10.1515/9781400883868Suche in Google Scholar
[5] G. W. Kattawar and G. N. Plass, Radiance and polarization of multiple scattered light from haze and clouds. Applied Optics7 (1968), No. 8, 1519–1527.10.1364/AO.7.001519Suche in Google Scholar PubMed
[6] M. Kerscher, W. Krichbaumer, M. Noormohammadian, and U. G. Oppel, Polarized multiply scattered LIDAR signals. Optical Review2 (1995), Issue 4, 304–307.10.1007/s10043-995-0304-7Suche in Google Scholar
[7] G. Z. Lotova, Monte Carlo algorithms for calculation of diffusive characteristics of an electron avalanche in gases. Russ. J. Numer. Anal. Math. Modelling31 (2011), No. 6, 369–377.10.1515/rnam-2016-0034Suche in Google Scholar
[8] G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics. Springer, Berlin–Heidelberg, 1980.10.1007/978-3-540-35237-2Suche in Google Scholar
[9] G. A. Mikhailov, Optimization of Weighted Monte Carlo Methods. Springer, Berlin–Heidelbetg, 1992.10.1007/978-3-642-75981-9Suche in Google Scholar
[10] G. A. Mikhailov, Parametric Estimates by the Monte Carlo Method. VSP, Utrecht, The Netherlands, 1999.10.1515/9783110941951Suche in Google Scholar
[11] G. A. Mikhailov and S. A. Rozhenko, Minimax optimization of numerical-statistical ‘method of similar trajectories’. Doklady Rus. Akad. Nauk446 (2012), No. 1, 15–17 (in Russian).10.1134/S1064562412050055Suche in Google Scholar
[12] G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Modelling. Monte Carlo Methods: A Tutorial. Akademiya, Moscow, 2006 (in Russian).Suche in Google Scholar
[13] G. A. Mikhailov, S. A. Ukhinov, and A. S. Chimaeva, Variance of the standard vector Monte Carlo estimator in the theory of polarized radiation transfer. Zh. Vychisl. Matem. Matem. Fiz. 46 (2006), No. 11, 2199–2212 (in Russian).10.1134/S0965542506110145Suche in Google Scholar
[14] S. M. Prigarin, Fundamentals of Statistical Modelling of Polarized Optical Radiation Transfer. Novosibirsk State Univ., Novosibirsk, 2010 (in Russian).Suche in Google Scholar
[15] J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, Three Monte Carlo programs of polarized light transport into scattering media: Part I. Optics Express13 (2005), No. 12, 4420–4438.10.1364/OPEX.13.004420Suche in Google Scholar
[16] G. V. Rozenberg, Stokes vector-parameter. Uspekhi Fiz. NaukLVI (1955), No. 1, 77–110 (in Russian).10.3367/UFNr.0056.195505c.0077Suche in Google Scholar
[17] V. V. Sobolev, Transfer of Radiant Energy in Atmospheres of Stars and Planets. GITTL, Moscow, 1956 (in Russian).Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The approach of ‘successive approximations over characteristic interactions’ for inverse problems of nuclear-geophysical technologies
- Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling
- Preconditioning for diffusion problem with small size high resolution inclusions
- Comparative analysis of vector algorithms for statistical modelling of polarized radiative transfer process
Artikel in diesem Heft
- Frontmatter
- The approach of ‘successive approximations over characteristic interactions’ for inverse problems of nuclear-geophysical technologies
- Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling
- Preconditioning for diffusion problem with small size high resolution inclusions
- Comparative analysis of vector algorithms for statistical modelling of polarized radiative transfer process